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Enthought ® Scientific Computing with Python [Advanced Topics] Eric Jones Enthought Travis Oliphant

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1 enthought ® Scientific Computing with Python [Advanced Topics] Eric Jones Enthought Travis Oliphant Brigham Young University

2 enthought ® Topics Python as Glue Wrapping Fortran Code Wrapping C/C++ Parallel Programming

3 enthought ® Python as “Glue”

4 enthought ® Why Python for glue? Python reads almost like “pseudo-code” so it’s easy to pick up old code and understand what you did. Python has dynamic typing and dynamic binding --- allows very flexible coding. Python is object oriented. Python has high-level data structures like lists, dictionaries, strings, and arrays all with useful methods. Python has a large module library (“batteries included”) and common extensions covering internet protocols and data, image handling, and scientific analysis. Python development is 5-10 times faster than C/C++ and 3-5 times faster than Java

5 enthought ® Electromagnetics Example (1)Parallel simulation (2)Create plot (3)Build HTML page (4)FTP page to Web Server (5) users that results are available.

6 enthought ® How is Python glue?

7 enthought ® Why is Python good glue? Python can be embedded into any C or C++ application Provides your legacy application with a powerful scripting language instantly. Python can interface seamlessly with Java –Jython –JPE Python can interface with critical C/C++ and Fortran subroutines –Rarely will you need to write a main-loop again. –Python does not directly call the compiled routines, it uses interfaces (written in C or C++) to do it --- the tools for constructing these interface files are fantastic (sometimes making the process invisible to you).

8 enthought ® Tools C/C++ Integration –SWIG –SIP –Pyrex –boost –weave FORTRAN Integration –f2py –PyFort

9 enthought ® f2py Author: Pearu Peterson at Center for Nonlinear Studies Tallinn, Estonia Automagically “wraps” Fortran 77/90/95 libraries for use in Python. Amazing. f2py is specifically built to wrap Fortran functions using NumPy arrays.

10 enthought ® Simplest f2py Usage Fortran File fcopy.f Python Extension Module Python Extension Module f2py –c fcopy.f –m fcopy Compile code and build an extension module Name the extension module fcopy.

11 enthought ® Simplest Usage Result Fortran file fcopy.f C SUBROUTINE FCOPY(AIN,N,AOUT) C DOUBLE COMPLEX AIN(*) INTEGER N DOUBLE COMPLEX AOUT(*) DO 20 J = 1, N AOUT(J) = AIN(J) 20 CONTINUE END >>> a = rand(1000) + 1j*rand(1000) >>> b = zeros((1000,),’D’) >>> fcopy.fcopy(a,1000,b) >>> import fcopy >>> info(fcopy) This module 'fcopy' is auto-generated with f2py (version: ). Functions: fcopy(ain,n,aout) >>> info(fcopy.fcopy) fcopy - Function signature: fcopy(ain,n,aout) Required arguments: ain : input rank-1 array('D') with bounds (*) n : input int aout : input rank-1 array('D') with bounds (*) Looks exactly like the Fortran --- but now in Python!

12 enthought ® More Sophisticated Fortran File fcopy.f Python Extension Module Python Extension Module f2py fcopy.f –h fcopy.pyf –m fcopy Interface File fcopy.pyf hand edit f2py -c fcopy.pyf fcopy.f

13 enthought ® More Sophisticated Interface file fcopy.pyf ! -*- f90 -*- python module fcopy ! in interface ! in :fcopy subroutine fcopy(ain,n,aout) ! in :fcopy:fcopy.f double complex dimension(n), intent(in) :: ain integer, intent(hide),depend(ain) :: n=len(ain) double complex dimension(n),intent(out) :: aout end subroutine fcopy end interface end python module fcopy ! This file was auto-generated with f2py (version: ). ! See fcopy - Function signature: aout = fcopy(ain) Required arguments: ain : input rank-1 array('D') with bounds (n) Return objects: aout : rank-1 array('D') with bounds (n) More Pythonic behavior >>> a = rand(100,’F’) >>> b = fcopy.fcopy(a) >>> print b.typecode() ‘D’ Give f2py some hints as to what these variables are used for and how they may be related in Python.

14 enthought ® Simply Sophisticated Fortran File fcopy.f hand edit Python Extension Module Python Extension Module f2py –c fcopy.f –m fcopy Compile code and build an extension module Name the extension module fcopy.

15 enthought ® Simply Sophisticated Fortran file fcopy2.f C SUBROUTINE FCOPY(AIN,N,AOUT) C CF2PY INTENT(IN), AIN CF2PY INTENT(OUT), AOUT CF2PY INTENT(HIDE), DEPEND(A), N=LEN(A) DOUBLE COMPLEX AIN(*) INTEGER N DOUBLE COMPLEX AOUT(*) DO 20 J = 1, N AOUT(J) = AIN(J) 20 CONTINUE END >>> a = rand(1000) >>> import fcopy >>> b = fcopy.fcopy(a) >>> import fcopy >>> info(fcopy.fcopy) fcopy - Function signature: aout = fcopy(ain) Required arguments: ain : input rank-1 array('D') with bounds (n) Return objects: aout : rank-1 array('D') with bounds (n) Much more Python like! A few directives can help f2py interpret the source.

16 enthought ® Saving the Module C-File Library of Fortran Files *.f Interface File flib.pyf hand edited C-extension Module flibmodule.c f2py –h alib.pyf –m alib *.ff2py alib.pyf f2py –c alibmodule.c *.f f2py –c alibmodule.c –l alib Library libflib.a Shared extension Module compile either one

17 enthought ® Multidimensional array issues Python and Numeric use C conventions for array storage (row major order). Fortran uses column major ordering. Numeric: A[0,0], A[0,1], A[0,2],…, A[N-1,N-2], A[N-1,N-1] (last dimension varies the fastest) Fortran: A(1,1), A(2,1), A(3,1), …, A(N-1,N), A(N,N) (first dimension varies the fastest) f2py handles the conversion back and forth between the representations if you mix them in your code. Your code will be faster, however, if you can avoid mixing the representations (impossible if you are calling out to both C and Fortran libraries that are interpreting matrices differently).

18 enthought ® How do I distribute this great new extension module? Recipient must have f2py and scipy_distutils installed (both are simple installs) Create file Distribute *.f files with file. Optionally distribute *.pyf file if you’ve spruced up the interface in a separate interface file. scipy_distutils Supported Compilers g77, Compaq Fortran, VAST/f90 Fortran, Absoft F77/F90, Forte (Sun), SGI, Intel, Itanium, NAG, Lahey, PG

19 enthought ® In scipy.stats there is a function written entirely in Python >>> info(stats.morestats._find_repeats) _find_repeats(arr) Find repeats in the array and return a list of the repeats and how many there were. Complete Example Goal: Write an equivalent fortran function and link it in to Python with f2py so it can be distributed with scipy_base (which uses scipy_distutils) and be available for stats. Python algorithm uses sort and so we will need a fortran function for that, too.

20 enthought ® Complete Example Fortran file futil.f C Sorts an array arr(1:N) into SUBROUTINE DQSORT(N,ARR) CF2PY INTENT(IN,OUT,COPY), ARR CF2PY INTENT(HIDE), DEPEND(ARR), N=len(ARR) INTEGER N,M,NSTACK REAL*8 ARR(N) PARAMETER (M=7, NSTACK=100) INTEGER I,IR,J,JSTACK, K,L, ISTACK(NSTACK) REAL*8 A,TEMP … END C Finds repeated elements of ARR SUBROUTINE DFREPS(ARR,N,REPLIST,REPNUM,NLIST) CF2PY INTENT(IN), ARR CF2PY INTENT(OUT), REPLIST CF2PY INTENT(OUT), REPNUM CF2PY INTENT(OUT), NLIST CF2PY INTENT(HIDE), DEPEND(ARR), N=len(ARR) REAL*8 REPLIST(N), ARR(N) REAL*8 LASTVAL INTEGER REPNUM(N) INTEGER HOWMANY, REPEAT, IND, NLIST, NNUM … END #Lines added to #add futil module sources = [os.path.join(local_path, 'futil.f'] name = dot_join(package,’futil’) ext = Extension(name,sources) config['ext_modules'].append(ext) #Lines added to # (under stats) import futil def find_repeats(arr): """Find repeats in arr and return (repeats, repeat_count) """ v1,v2, n = futil.dfreps(arr) return v1[:n],v2[:n]

21 enthought ® Complete Example Try It Out!! >>> from scipy import * >>> a = stats.randint(1,30,size=1000) >>> reps, nums = find_repeats(a) >>> print reps [ ] >>> print nums [ ] New function is 25 times faster than the plain Python version

22 enthought ® Complete Example Packaged for Individual release #!/usr/bin/env python # File: from scipy_distutils.core import Extension ext = Extension(name = 'futil', sources = ['futil.f']) if __name__ == "__main__": from scipy_distutils.core import setup setup(name = 'futil', description = "Utility fortran functions", author = "Travis E. Oliphant", author_ = ext_modules = [ext] ) # End of python install With futil.f in current directory this builds and installs on any platform with a C compiler and a fortran compiler that scipy_distutils recognizes.

23 enthought ® Weave

24 enthought ® weave weave.blitz() Translation of Numeric array expressions to C/C++ for fast execution weave.inline() Include C/C++ code directly in Python code for on-the-fly execution weave.ext_tools Classes for building C/C++ extension modules in Python

25 enthought ® >>> import weave >>> a=1 >>> weave.inline('std::cout << a << std::endl;',['a']) sc_f08dc0f70451ecf9a9c9d4d0636de3670.cpp Creating library 1 >>> weave.inline('std::cout << a << std::endl;',['a']) 1 >>> a='qwerty' >>> weave.inline('std::cout << a << std::endl;',['a']) sc_f08dc0f70451ecf9a9c9d4d0636de3671.cpp Creating library qwerty >>> weave.inline('std::cout << a << std::endl;',['a']) qwerty weave.inline

26 enthought ® >>> import weave >>> a = 1 >>> support_code = ‘int bob(int val) { return val;}’ >>> weave.inline(‘return_val = bob(a);’,['a'],support_code=support_code) sc_19f0a1876e e9104c0cce4f00c0.cpp Creating library 1 >>> a = 'string' >>> weave.inline(‘return_val = bob(a);’,['a'],support_code = support_code) sc_19f0a1876e e9104c0cce4f00c1.cpp C:\DOCUME~1\eric\LOCALS~1\Temp\python21_compiled\sc_19f0a1876e e9104c0cce4 f00c1.cpp(417) : error C2664: 'bob' : cannot convert parameter 1 from 'class Py: :String' to 'int' No user-defined-conversion operator available that can perform this conversion, or the operator cannot be called Traceback (most recent call last): weave.build_tools.CompileError: error: command '"C:\Program Files\Microsoft Visu al Studio\VC98\BIN\cl.exe"' failed with exit status 2 Support code example

27 enthought ® import string from weave import ext_tools def build_ex1(): ext = ext_tools.ext_module('_ex1') # Type declarations– define a sequence and a function seq = [] func = string.upper code = """ py::tuple args(1); py::list result(seq.length()); for(int i = 0; i < seq.length();i++) { args[0] = seq[i]; result[i] = PyEval_CallObject(func,py::tuple(args[0])); } return_val = result; """ func = ext_tools.ext_function('my_map',code,['func','seq']) ext.add_function(func) ext.compile() try: from _ex1 import * except ImportError: build_ex1() from _ex1 import * if __name__ == '__main__': print my_map(string.lower,['asdf','ADFS','ADSD']) ext_tools example

28 enthought ® >>> c = a + b + c // c code // tmp1 = a + b tmp1 = malloc(len_a * el_sz); for(i=0; i < len_a; i++) tmp1[i] = a[i] + b[i]; // tmp2 = tmp1 + c tmp2 = malloc(len_c * el_sz); for(i=0; i < len_c; i++) tmp2[i] = tmp1[i] + c[i]; Efficiency Issues FAST, IDIOMATIC C CODEPSEUDO C FOR STANDARD NUMERIC EVALUATION >>> c = a + b + c // c code // 1. loops “fused” // 2. no memory allocation for(i=0; i < len_a; i++) c[i] = a[i] + b[i] + c[i]; tmp1 tmp2

29 enthought ® Finite Difference Equation MAXWELL’S EQUATIONS: FINITE DIFFERENCE TIME DOMAIN (FDTD), UPDATE OF X COMPONENT OF ELECTRIC FIELD PYTHON VERSION OF SAME EQUATION, PRE-CALCULATED CONSTANTS ex[:,1:,1:] = ca_x[:,1:,1:] * ex[:,1:,1:] + cb_y_x[:,1:,1:] * (hz[:,1:,1:] - hz[:,:-1,:]) - cb_z_x[:,1:,1:] * (hy[:,1:,1:] - hy[:,1:,:-1])

30 enthought ® WEAVE.BLITZ VERSION OF SAME EQUATION >>> from scipy import weave >>> # >>> expr = “ex[:,1:,1:] = ca_x[:,1:,1:] * ex[:,1:,1:]”\ “+ cb_y_x[:,1:,1:] * (hz[:,1:,1:] - hz[:,:-1,:])”\ “- cb_z_x[:,1:,1:] * (hy[:,1:,1:] - hy[:,1:,:-1])” >>> weave.blitz(expr) weave.blitz compiles array expressions to C/C++ code using the Blitz++ library. weave.blitz

31 enthought ® weave.blitz benchmarks EquationNumeric (sec) Inplace (sec) compiler (sec) Speed Up Float (4 bytes) a = b + c (512,512) a = b + c + d (512x512) pt. avg filter (512x512) FDTD (100x100x100) Double (8 bytes) a = b + c (512,512) a = b + c + d (512x512) pt. avg filter (512x512) FDTD (100x100x100) Pentium II, 300 MHz, Python 2.0, Numeric Speed-up taken as ratio of scipy.compiler to standard Numeric runs.

32 enthought ® PURE PYTHON2000 SECONDS for i in range(1, nx-1): for j in range(1, ny-1): tmp = u[i,j] u[i,j] = ((u[i-1, j] + u[i+1, j])*dy2 + (u[i, j-1] + u[i, j+1])*dx2) / (2.0*(dx2 + dy2)) diff = u[i,j] – tmp err = err + diff**2 Weave case study: An iterative solver for Laplace’s Equation weave and Laplace’s equation Thanks to Prabhu Ramachandran for designing and running this example. His complete write-up is available at:

33 enthought ® WEAVE.BLITZ 10.2 SECONDS old_u = u.copy() # needed to compute the error. u[1:-1, 1:-1] = ((u[0:-2, 1:-1] + u[2:, 1:-1])*dy2 + (u[1:-1, 0:-2] + u[1:-1, 2:])*dx2) * dnr_inv err = sum(dot(old_u – u)) weave and Laplace’s equation USING NUMERIC29.0 SECONDS old_u = u.copy() # needed to compute the error. expr = ””” \ u[1:-1, 1:-1] = ((u[0:-2, 1:-1] + u[2:, 1:-1])*dy2 + (u[1:-1, 0:-2] + u[1:-1, 2:])*dx2) * dnr_inv ””” weave.inline(expr,size_check=0) err = sum((old_u – u)**2)

34 enthought ® code = """ #line 120 "" (This is only useful for debugging) double tmp, err, diff; err = 0.0; for (int i=1; i

35 enthought ® Laplace Benchmarks MethodRun Time (sec) Speed Up Pure Python  0.02 Numeric weave.blitz weave.inline weave.inline (fast) Python/Fortran (with f2py) Pure C++ Program Debian Linux, Pentium III, 450 MHz, Python 2.1, 192 MB RAM Laplace solve for 500x500 grid and 100 iterations Speed-up taken as compared to Numeric

36 enthought ® SWIG

37 enthought ® SWIG Author: David Beazley at Univ. of Chicago Automatically “wraps” C/C++ libraries for use in Python. Amazing. SWIG uses interface files to describe library functions –No need to modify original library code –Flexible approach allowing both simple and complex library interfaces Well Documented

38 enthought ® SWIG Process Interface File lib.i C Extension File lib_wrap.c Python Extension Module Python Extension Module SWIG compile Library Files *.h files*.c files compile Writing this is your responsibility (kinda)

39 enthought ® Simple Example #ifndef FACT_H #define FACT_H int fact(int n); #endif #include “fact.h” int fact(int n) { if (n <=1) return 1; else return n*fact(n-1); } fact.h fact.c example.i // Define the modules name %module example // Specify code that should // be included at top of // wrapper file. %{ #include “fact.h” %} // Define interface. Easy way // out - Simply include the // header file and let SWIG // figure everything out. %include “fact.h”

40 enthought ® Building the Module LINUX # Create example_wrap.c file ej]$ swig –python example.i # Compile library and example_wrap.c code using # “position independent code” flag ej]$ gcc –c –fpic example_wrap.c fact.c \ –I/usr/local/include/python2.1\ –I/usr/local/lib/python2.1/config # link as a shared library. ej]$ gcc –shared example_wrap.o fact.o\ -o # test it in Python ej]$ python... >>> import example >>> example.fact(4) 24 For notes on how to use SWIG with VC++ on Windows, see

41 enthought ® The Wrapper File example_wrap.c static PyObject *_wrap_fact(PyObject *self, PyObject *args) { PyObject *resultobj; int arg0 ; int result ; /* parse the Python input arguments and extract */ if(!PyArg_ParseTuple(args,"i:fact",&arg0)) return NULL; /* call the actual C function with arg0 as the argument*/ result = (int )fact(arg0); /* Convert returned C value to Python type and return it*/ resultobj = PyInt_FromLong((long)result); return resultobj; } first arg in args read into arg0 as int name of function to return in case of error

42 enthought ® SWIG Example 2 int* vect(int x,int y,int z); int sum(int* vector); #include #include “vect.h” int* vect(int x,int y, int z){ int* res; res = malloc(3*sizeof(int)); res[0]=x;res[1]=y;res[2]=z; return res; } int sum(int* v) { return v[0]+v[1]+v[2]; } vect.h vect.c example2.i Identical to example.i if you replace “fact” with “vect”. TEST IN PYTHON >>> from example2 import * >>> a = vect(1,2,3) >>> sum(a) 6#works fine! # Let’s take a look at the # integer array a. >>> a '_813d880_p_int' # WHAT THE HECK IS THIS???

43 enthought ® Complex Objects in SWIG SWIG treats all complex objects as pointers. These C pointers are mangled into string representations for Python’s consumption. This is one of SWIG’s secrets to wrapping virtually any library automatically, But… the string representation is pretty primitive and makes it “un-pythonic” to observe/manipulate the contents of the object. Enter typemaps

44 enthought ® Typemaps example_wrap.c static PyObject *_wrap_sum(PyObject *self, PyObject *args) {... if(!PyArg_ParseTuple(args,"O:sum",&arg0)) return NULL;... result = (int )sum(arg0);... return resultobj; } Typemaps allow you to insert “type conversion” code into various location within the function wrapper. Not for the faint of heart. Quoting David: “You can blow your whole leg off, including your foot!”

45 enthought ® Typemaps The result? Standard C pointers are mapped to NumPy arrays for easy manipulation in Python. YET ANOTHER EXAMPLE – NOW WITH TYPEMAPS >>> import example3 >>> a = example3.vect(1,2,3) >>> a # a should be an array now. array([1, 2, 3], 'i') # It is! >>> example3.sum(a) 6 The typemaps used for example3 are included in the handouts. Another example that wraps a more complicated C function used in the previous VQ benchmarks is also provided. It offers more generic handling 1D and 2D arrays.

46 enthought ® Parallel Programming in Python

47 enthought ® Parallel Computing Tools Python has threads (sort’a) pyMPI( pyre (CalTech) PyPAR ( SCIENTIFIC ( COW (

48 enthought ® Cluster Computing with Python Pure Python Approach Easy to Use Suitable for “embarrassingly” parallel tasks pyMPI (Message Passing Interface) Developed by Patrick Miller, Martin Casado et al. at Lawrence Livermore National Laboratories De-facto industry standard for high-performance computing Vendor optimized libraries on “Big Iron” Possible to integrate existing HPFortran and HPC codes such as Scalapack (parallel linear algebra) into Python.

49 enthought ® Threads Python threads are built on POSIX and Windows threads (hooray!) Python threads share a “lock” that prevents threads from invalid sharing Threads pass control to another thread –every few instructions –during blocking I/O (if properly guarded) –when threads die

50 enthought ® The “threading” module from threading import Thread –a lower level thread library exists, but this is much easier to use a thread object can “fork” a new execution context and later be “joined” to another you provide the thread body either by creating a thread with a function or by subclassing it

51 enthought ® Making a thread we will work at the prompt! >>> from threading import * >>> def f(): print ‘hello’ >>> T = Thread(target=f) >>> T.start()

52 enthought ® Thread operations currentThread() T.start() T.join() T.getName() / T.setName() T.isAlive() T.isDaemon() / T.setDaemon()

53 enthought ® Passing arguments to a thread >>> from threading import * >>> def f(a,b,c): print ‘hello’,a,b,c >>> T = Thread(target=f,args=(11,22),kwargs={‘c’: ) >>> T.start()

54 enthought ® Subclassing a thread from threading import * class myThread(Thread): def __init__(self,x,**kw): Thread.__init__(self,**kw) #FIRST! self.x = x def run(): print self.getName() print ‘I am running’,self.x T = myThread(100) T.start() NOTE: Only __init__ and run() are available for overload

55 enthought ® CAUTION! Threads are really co-routines! Only one thread can operate on Python objects at a time Internally, threads are switched If you write extensions that are intended for threading, use –PY_BEGIN_ALLOW_THREADS –PY_END_ALLOW_THREADS

56 enthought ® cow

57 enthought ® Electromagnetic Scattering Inputs environment, target mesh, and multiple frequencies Mem:KB to Mbytes Computation N 3 CPU N 2 storage Time:a few seconds to days Mem: MB to GBytes Outputs Radar Cross Section values Mem: KB to MBytes SMALLLARGE!SMALL

58 enthought ® 58

59 enthought ® Cluster Creation Port numbers below 1024 are reserved by the OS and generally must run as ‘root’ or ‘system’. Valid port numbers are between Be sure another program is not using the port you choose.

60 enthought ® Starting remote processes start() uses ssh to start an interpreter listening on port on each remote machine

61 enthought ® Dictionary Behavior of Clusters

62 enthought ® Dictionary Behavior of Clusters

63 enthought ® cluster.apply()

64 enthought ® cluster.exec_code()

65 enthought ® cluster.loop_apply()

66 enthought ® Cluster Method Review apply(function, args=(), keywords=None) –Similar to Python’s built-in apply function. Call the given function with the specified args and keywords on all the worker machines. Returns a list of the results received from each worker. exec_code(code, inputs=None, returns=None) –Similar to Python’s built-in exec statement. Execute the given code on all remote workers as if it were typed at the command line. inputs is a dictionary of variables added to the global namespace on the remote workers. returns is a list of variable names (as strings) that should be returned after the code is executed. If returns contains a single variable name, a list of values is returned by exec_code. If returns is a sequence of variable names, exec_code returns a list of tuples.

67 enthought ® Cluster Method Review loop_apply(function,loop_var,args=(), keywords=None) –Call function with the given args and keywords. One of the arguments or keywords is actually a sequence of arguments. This sequence is looped over, calling function once for each value in the sequence. loop_var indicates which variable to loop over. If an integer, loop_var indexes the args list. If a string, it specifies a keyword variable. The loop sequence is divided as evenly as possible between the worker nodes and executed in parallel. loop_code(code, loop_var, inputs=None, returns=None) –Similar to exec_code and loop_apply. Here loop_var indicates a variable name in the inputs dictionary that should be looped over.

68 enthought ® Cluster Method Review ps(sort_by=‘cpu’,**filters) –Display all the processes running on the remote machine much like the ps Unix command. sort_by indicates which field to sort the returned list. Also keywords allow the list to be filtered so that only certain processes are displayed. info() –Display information about each worker node including its name, processor count and type, total and free memory, and current work load.

69 enthought ® Query Operations >>> MACHINE CPU GHZ MB TOTAL MB FREE LOAD s0 2xP s1 2xP s2 2xP >>>'ej',cpu='>50') MACHINE USER PID %CPU %MEM TOTAL MB RES MB CMD s0 ej python... s1 ej python... s2 ej python...

70 enthought ® Simple FFT Benchmark >>> b = fft(a) # a is a 2D array: 8192 x 512 (1) STANDARD SERIAL APPROACH TO 1D FFTs (2) PARALLEL APPROACH WITH LOOP_APPLY >>> b = cluster.loop_apply(fft,0,(a,)) (3) PARALLEL SCATTER/COMPUTE/GATHER APPROACH >>> cluster.import_all(‘FFT’) # divide a row wise amongst workers >>> cluster.row_split('a',a) # workers calculate fft of small piece of a and stores as b. >>> cluster.exec_code('b=fft(a)') # gather the b values from workers back to master. >>> b = cluster.row_gather('b')

71 enthought ® FFT Benchmark Results MethodCPUsRun Time (sec) Speed Up Efficiency (1) standard (2) loop_apply % (3) scatter/compute/gather % Test Setup: The array a is 8192 by 512. fft s are applied to each row independently as is the default behavior of the FFT module. The cluster consists of 16 dual Pentium II 450 MHz machines connected using 100 Mbit ethernet.

72 enthought ® FFT Benchmark Results MethodCPUsRun Time (sec) Speed Up Efficiency (1) standard (2) loop_apply % (3) scatter/compute/gather % (3) compute alone % (3) compute alone % (3) compute alone % (3) compute alone % Moral: If data can be distributed among the machines once and then manipulated in place, reasonable speed-ups are achieved.

73 enthought ® Electromagnetics EM Scattering ProblemCPUsRun Time (sec) Speed Up Efficiency Small Buried Sphere 64 freqs, 195 edges % Land Mine 64 freqs, 1152 edges %

74 enthought ® Serial vs. Parallel EM Solver def serial(solver,freqs,angles): results = [] for freq in freqs: # single_frequency handles calculation details res = single_frequency(solver,freq,angles) results.append(res) return results SERIAL VERSION PARALLEL VERSION def parallel(solver,freqs,angles,cluster): # make sure cluster is running cluster.start(force_restart = 0) # bundle arguments for loop_apply call args = (solver,freqs,angles) # looping handled by loop_apply results = cluster.loop_apply(single_frequency,1,args) return results

75 enthought ® pyMPI

76 enthought ® Simple MPI Program # output is asynchronous % mpirun -np 4 pyMPI >>> import mpi >>> print mpi.rank # force synchronization >>> mpi.synchronizedWrite(mpi.rank, ’\n’)

77 enthought ® Broadcasting Data import mpi import math if mpi.rank == 0: data = [sin(x) for x in range(0,10)] else: data = None common_data = mpi.bcast(data)

78 enthought ® mpi.bcast() bcast() broadcasts a value from the “root” process (default is 0) to all other processes bcast’s arguments include the message to send and optionally the root sender the message argument is ignored on all processors except the root

79 enthought ® Scattering an Array # You can give a little bit to everyone import mpi from math import sin,pi if mpi.rank == 0: array = [sin(x*pi/99) for x in range(100)] else: array = None # give everyone some of the array local_array = mpi.scatter(array)

80 enthought ® mpi.scatter() scatter() splits an array, list, or tuple evenly (roughly) across all processors the function result is always a [list] an optional argument can change the root from rank 0 the message argument is ignored on all processors except the root

81 enthought ® Gathering wandering data # Sometimes everyone has a little data to bring # together import mpi import math local_data = [sin(mpi.rank*x*pi/99) for x in range(100)] print local_data root_data = mpi.gather(local_data) print root_data

82 enthought ® mpi.gather() / mpi.allgather() gather appends lists or tuples into a master list on the root process if you want it on all ranks, use mpi.allgather() instead every rank must call the gather()

83 enthought ® Reductions # You can bring data together in interesting ways import mpi x_cubed = mpi.rank**3 sum_x_cubed = mpi.reduce(x_cubed,mpi.SUM)

84 enthought ® mpi.reduce() / mpi.allreduce() The reduce (and allreduce) functions apply an operator across data from all participating processes You can use predefined functions –mpi.SUM, mpi.MIN, mpi.MAX, etc… you can define your own functions too you may optionally specify an initial value

85 enthought ® 3D Visualization with VTK

86 enthought ® Visualization with VTK Visualization Toolkit from Kitware – Large C++ class library –Wrappers for Tcl, Python, and Java –Extremely powerful, but… –Also complex with a steep learning curve

87 enthought ® VTK Gallery

88 enthought ® VTK Pipeline PIPELINEOUTPUT Pipeline view from Visualization Studio at

89 enthought ® Cone Example SETUP # VTK lives in two modules from vtk import * # Create a renderer renderer = vtkRenderer() # Create render window and connect the renderer. render_window = vtkRenderWindow() render_window.AddRenderer(renderer) render_window.SetSize(300,300) # Create Tkinter based interactor and connect render window. # The interactor handles mouse interaction. interactor = vtkRenderWindowInteractor() interactor.SetRenderWindow(render_window)

90 enthought ® Cone Example (cont.) PIPELINE # Create cone source with 200 facets. cone = vtkConeSource() cone.SetResolution(200) # Create color filter and connect its input # to the cone's output. color_filter = vtkElevationFilter() color_filter.SetInput(cone.GetOutput()) color_filter.SetLowPoint(0,-.5,0) color_filter.SetHighPoint(0,.5,0) # map colorized cone data to graphic primitives cone_mapper = vtkDataSetMapper() cone_mapper.SetInput(color_filter.GetOutput())

91 enthought ® Cone Example (cont.) DISPLAY # Create actor to represent our # cone and connect it to the # mapper cone_actor = vtkActor() cone_actor.SetMapper(cone_mapper) # Assign actor to # the renderer. renderer.AddActor(cone_actor) # Initialize interactor # and start visualizing. interactor.Initialize() interactor.Start()

92 enthought ® Mesh Generation POINTS AND CELLS points id x y z temp triangles id x y z # Convert list of points to VTK structure verts = vtkPoints() temperature = vtkFloatArray() for p in points: verts.InsertNextPoint(p[0],p[1],p[2]) temperature.InsertNextValue(p[3]) # Define triangular cells from the vertex # “ids” (index) and append to polygon list. polygons = vtkCellArray() for tri in triangles: cell = vtkIdList() cell.InsertNextId(tri[0]) cell.InsertNextId(tri[1]) cell.InsertNextId(tri[2]) polygons.InsertNextCell(cell)

93 enthought ® Mesh Generation POINTS AND CELLS # Create a mesh from these lists mesh = vtkPolyData() mesh.SetPoints(verts) mesh.SetPolys(polygons) mesh.GetPointData().SetScalars( \... temperature) # Create mapper for mesh mapper = vtkPolyDataMapper() mapper.SetInput(mesh) # If range isn’t set, colors are # not plotted. mapper.SetScalarRange( \... temperature.GetRange()) Code for temperature bar not shown.

94 enthought ® VTK Demo

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